Hello there,
Lets try to clear up some of the mysteries about the skin effect, first.
The simplest way to look at skin effect in a round cross section wire is that at some fixed frequency the wire, which resembles a rod, only conducts in the outer shell which is closer to the surface, and much less near the very axial center of the rod. This is a simplified view but is accurate enough to use for now.
This "outer shell" would look like a pipe, which is hollow in the center as all pipes are, and so the conduction is limited to the metal of this pipe which might be much thinner than the rod. Because it is much thinner, the AC resistance is higher than the DC resistance. A side effect is that the metal (usually copper) that occupies the center of the rod is mostly wasted because it doesnt conduct much.
This in no way suggests that a larger diameter wire somehow has more AC resistance than a smaller diameter wire, because at a fixed frequency as we let the diameter increase the area involved in the major part of the conduction also increases, and thus lowers the AC resistance. So a larger diameter wire always has less DC and less AC resistance than a smaller diameter. So using a larger diameter wire will always increase the Q of the coil.
What is wasted however is the copper bulk that occupies the central part of the wire, and also the bobbin or window space on the core. Sometimes this doesnt matter, because it is a small RF coil and even with larger wire it's still quite small. But with a core there is the window space to consider, where the larger wire takes up more of the window and so less turns can fit onto the core.
Now using the simplified theory of the skin depth, if we use a wire of radius equal to the skin depth, there is less copper wasted because there is significant conduction in most parts of the cross section of the wire. This means the average current density is going to be higher on average, and since the window area is limited we usually want the maximum current density, unless of course we have room to spare. So enter in the Litz wire, which will have smaller strands of wire to make up a larger wire. If all the radii of all the strands are equal in size to the skin depth, then the wire should conduct more than a larger diameter wire, and thus result in a higher Q, and take up less room in the window area of the core.
We just talked about this in depth on another site, so i have a quick example here.
At 100kHz, an AWG #26 gauge wire would be considered to conduct the AC current almost the same as the DC current (although a more accurate calculation yields about a 25 percent decrease in conduction).
At 100kHz, an AWG #22 gauge wire (going down 4 wire sizes) would waste more copper and take up more room, but conduct twice as well for AC as the #26 wire.
The skin depth for copper wire can be approximated from this simple formula:
d=1361/(6641*pi*sqrt(f))
where f is in Hertz and d is in meters.
A quick example for f=100kHz is d=0.21 millimeters.
Since f is in the denominator and we take the square root, this means a frequency 100 times greater will have skin depth sqrt(100)=10 times less, so at 10Mhz the skin depth would be 0.021 millimeters.
At 15MHz the skin depth would be about 0.017 millimeters, and twice this is 0.034mm, and that's about half the diameter of an AWG #40 gauge wire.
When the Litz wire is wound it is wound in a way so as to reduce the proximity effect, so i would think the conduction would still be better for Litz wire, provided you cant use a larger diameter wire.
We could estimate the various comparative Q for inductors made with different size wires.
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